Limits on the Time Evolution of Space Dimensions from Newton's Constant

TL;DR

This paper constrains the rate of change of extra spatial dimensions in a universe model with variable dimensions, using bounds on Newton's constant variation, and finds the model unlikely to be valid given current observational limits.

Contribution

It incorporates the effects of volume and surface area of extra dimensions into the analysis of Newton's constant variation, providing tighter bounds on the evolution of space dimensions.

Findings

The present rate of change of spatial dimensions is less than 10^{-14} yr^{-1}.

The spatial dimension at the Planck scale is constrained to be less than or equal to 3.09.

The results challenge the viability of the TVSD model based on observational bounds.

Abstract

Limits are imposed upon the possible rate of change of extra spatial dimensions in a decrumpling model Universe with time variable spatial dimensions (TVSD) by considering the time variation of (1+3)-dimensional Newton's constant. Previous studies on the time variation of (1+3)-dimensional Newton's constant in TVSD theory had not been included the effects of the volume of the extra dimensions and the effects of the surface area of the unit sphere in D-space dimensions. Our main result is that the absolute value of the present rate of change of spatial dimensions to be less than about 10^{-14}yr^{-1}. Our results would appear to provide a prima facie case for ruling the TVSD model out. We show that based on observational bounds on the present-day variation of Newton's constant, one would have to conclude that the spatial dimension of the Universe when the Universe was at the Planck scale to be less than or equal to 3.09. If the dimension of space when the Universe was at the Planck scale is constrained to be fractional and very close to 3, then the whole edifice of TVSD model loses credibility.